PORE SPACES -WHERE GW IS STORED AND MOVES THROUGH MATERIALS - PDF document

1 PORE SPACES -WHERE GW IS STORED AND MOVES THROUGH MATERIALS POROSITY (TOTAL) -% OF MATERIAL THAT IS VOIDSPorosity = V V - VOLOFVOIDS V V -TOTAL VOLUME 2 SOIL ENGINEERS USE VOID RATIO, SvVVe -VOL OF VOIDS-VOL OF SOLIDS Relationshipofvoidratioandporosity Relationship porosity 1ee1e METHODS OF MEASURING POROSITY (PD -PARTICLE DENSITY : M/LFD -FLUID DENSITY: M/LBD -BULK DENSITY : M/L) PD + __________________________________________OR (for fresh water in grams and cc’s) is fluid SW -SATURATED WEIGHT-TOTAL VOLDW -DRY WEIGHT_________________________________________DW -DRY WEIGHT V TOTALVOLUME TVDWSW 1- - TOTAL PD -PARTICLE DENSITY TTV*PDDW1)1(PDVDW 3 Given:Wet Bulk Density = 2.24 g/cmParticle Density = 2.65 g/cmFluid Density (FD) = 1.0 g/cmWhat is: T VDWSW TDW 1 )1(PDVDW ) PD + Porosity = ? T TV*PD 1 AndIf: Knowing:Wet Bulk Density = 2.24 g/cmParticle Density = 2.65 g/cmFluid Density (FD) = 1.0 g/cmPorosity = 0.25 ) PD + Total Volume = 25cmWhat is:Saturated Weight = ?Dry Weight = ? TVDWSW TV*PDDW1)1(PDVDW 4 PRIMARY POROSITY-FORMED CONTEMPORANEOUSLY WITH ROCKSECONDARY POROSITY-FORMED AFTER ROCK IS FORMED POROSITY DEPENDS ON:SHAPE AND ARRANGEMENT OF PARTICLESDEGREE OF SORTING (MIX OF PARTICLE SIZES) CEMENTATION OR COMPACTIONREMOVAL OF MATERIAL BY SOLUTIONFRACTURING AND JOINTING SHAPE AND ARRANGEMENT OF PARTICLESdepends on packing as well as shape -the spacing and mutual arrangement of particles within the mass-will influence not only porosity but alsodensity, bearing capacity, strength, amount fttlibilit o f se ttli ng, permea bilit -difficult to study withshapes are so varied, so consider spheres 5 Assume that you have two boxes that each have a volume of 8 cubic meters.Each box is filled with spheres in a cubic packing arrangement. Box number one is filled with spheres having a radius of 1 meter while the spheres in box number two have a radius of 0.5 meters Whihbdhthhihtl? c h b o you suppose h as hi h pore vo l ume ? 222 22 This is a bad drawing but I hope you get Calculate the porosity: the volume of a sphere is V=4/3 POROSITY CAN BE DECREASED FURTHER BY FILLING VOIDS WITH SMALLER PARTICLES SORTING (poor=lotsofsizeswell=fewsizes) SORTING (poor = = (poor = few sizes, well = lots of sizes)i.e. well graded has a gradation of sizesPOORLY SORTEDWELL GRADED WELL SORTEDPOORLY GRADED 6 CEMENTATION OR COMPACTION REMOVAL OF MATERIAL BY SOLUTIONFRACTURING AND JOINTING Generally INCREASES POROSITY Contributes to Fluid Flow% OF MEDIUM THAT IS INTERCONNECTED PORE SPACE T IVe V V -VOL OF INTERCONNECTED VOIDSMEASUREMENT OF EFFECTIVE POROSITY: GRAVITY DRAINAGE @ 100% RELATIVE HUMIDTRACER TEST -MONITOR RATE OF MOVEMENT OF A TAG ON THE WATER 7 Darcyvelocityis a DISCHARGE per unit AREAAverage LinearVelocity AQVDarcy velocity through the pores this governs rate of pollutant movement porosityeffectiveVVAQVDeDeearAverageLin Just pore Seepage VelocityInterstitial Velocity Entire face of the porous medium space v,pronounced ,v as repesentedOften Recall Darcy discharge calculation from the first class?Q = K __Head Difference______ Distance between Heads Q = 0.01 cm 0.19 m 6cm 0.75cm 1 liter 86400sec = 1.17 liter = 1 liter sec 0.63 m 1000cm3 day day day constant head What is the travel time for a drop of water from left to right if effective porosity is 31%? FINE SAND 0.63 m 0.4 m 6 cm0.75 cm 0.21 m effective porosity is 31% 8 WE CAN'T RECOVER ALL THE WATER FROM THE PORES,SO CONSIDER HOW MUCH WATER THEY WILL YIELDSPECIFIC YIELD-% OF TOTAL VOLUME THAT CAN BE DRAINED BY GRAVITYSPECIFIC RETENTION-% OF TOTAL VOLUME HELD AGAINST GRAVITY SRdemo BY DEFINITION -φ= SY + SR of Waterin various Zones 9 Zones of Different Water Occurrence Hygroscopic 0 % Sat 100% zonetype of water Degree of Saturation= volume water filled pores volume of all pores p th Zone of AerationCapillary Fringe PellicularGravitationalWater Capillary Water Phreatic Water WT Water Table Vadose Saturated Zone Confined Water consider the pressure conditions ABOVEWater Table ATMOSPHERIC (-)BELOW Water Table&#x-2.4; ATMOSPHERIC (+)WATER TABLE is the surface at which the pore water pressure is A 0 relative pressure elevation Water Table capillary (-) In a hydrostatic (still) system pressure increases with depth below the water table due to the weight of the overlying waterPascal’s Law: (-) tension atmospheric compression(+) hhgP 10 Pascal’s Law:P difference in hydrostatic pressure (pascals) attwopointsinafluidcolumn hhgP two a fluid density (kg mh's gravity at sea level (msh height of fluid above a datum (m), ordifference in elevation of two points in a fluid columnspecific weight Fluid does not support shear stress so pressure is transmitted equally throughout the fluid. Let’s convince ourselves LOCAL ATMOSPHERIC P + GAGEPGAGE PRESSUREP RELATIVE TO PREVAILING ATMOSPHERIC P ATMOSPHERIC PRESSUREDEFINED AS ZERO for many Hydrology calculations Standard Atmospheric Pressure =Pascalsor 14.7 lb/in http://en.wikipedia.org/wiki/Pascal 11 Calculate the pressure on your head if you stoodAt the bottom of a well with its:surface at sea level bottom at 600 ftwater level 50 ft below the surfacedetermine appropriate equation gatherconstants/properties gather / CAPILLARITY (suction or negative pressure)inter-molecular attraction at the liquid boundarythe attractive (wetting), or repulsive (non-wetting), force between the molecules of the liquid and solid Chi thtttifbt llfthliid C o h e a tt rac t ween es o f upward force of the attraction of the liquid to the solidwould cause the liquid to continue rising except that it is by downward force of gravity on the liquid InatubetheHEIGHTofRISEiscontrolledbytheSIZEofTUBE In a controlled because as radius increasesdownward force of gravity increases more rapidly than upward force of attraction of liquid to solid(note the area grows as rwhile the circumference grows as r) 12 Capillary Rise In a droplet within the liquid are attracted equally from all sidesmolecules near the surface are attracted toward the centeroftheliquidmass bythisnetforce center surface acts like a membraneof liquid forms a and liquid in a tube forms a 13 the capillary fringe will show hysteresis effectsHysteresis (dependent on history)describes a phenomenon which is dependent on previous historyas the water table moves up and down the capillary fringe will changeincharacter change Rise limited by larger pore Capillary rise g water table held in narrow pore wate held in narrow For a cylinder capillary pressure can be calculated as:= 2 (surface tension)cos radius rcos2h soh rcos2Pcc so height of capillary rise is h Surface Tension -force (perpendicular to the surface) along a The numerical value of surface tension depends on the nature of the fluid and solid 14 Let’s take a minute to think about unitsBeware! of your units .... that is BE AWARE of your unitsF = ma ...... W = Weight = mg gisgravitationalacceleration g weight has same units as force (not mass)Basic units: L M Tlength mass time meter kilogram second DerivedunitF - forceNNewton F , N Newton Basic units L F Tlength force timeft lb sfoot pound second Derived unit M -mass, S slug 1 Newton (N) of force will accelerate 1 kilogram mass (kgm) 1 meter per second squaredF = ma 1 Newton 1 kgm 1 m English Units (foot-slug-second)1 pound force (lbf) accelerates 1 slug mass 1 ft per second squareF = ma 1lbf1l 1ft 1 1 s it can be confusinggiven that one slug equals 32.2 lbm 15 Weight in US: a of water weighs 62.4 lbsIn Europe we say a cubic foot of water weighs 28.3 kgWe mean it has a mass of 28.3kg in earth’s gravity : It weighs 273NDensity is MASS per VOLUME3 Specific Weight is WEIGHT per VOLUME3 WetendtouseDensitywhenworkinginSIand when working What looks like Specific Weight in English UnitsDensity of water is 1.94 slugs/ftRecall 1 pound force (lbf) accelerates 1 slug mass 1 ft per second squared ft ftsluglbf22seclbf 1per slug 1is thereso sec 11 ft sec numerical value 32234.62sec2.32sec194.1ftlbfftftsluglbfftslugg 334.62 then lbm, 32.17 slug 1 given that so 94.1ftlbmftslug From your text, Fetter 16 Surface tension for distilled water in contact with air in a clean glass tube is 72.8 dynes/cm, contact angle is zero, cos is 11 dyne imparts an acceleration of 1 cm/secto a mass of 1 gramor an acceleration of g = 981 cm/secto 0.00102 grams force 2 2 72.8g d gf00102.0 223 2 2 ssgs rcos2hc Surface tension for distilled water in contact with air in a clean glass tube is 72.8 dynes/cm, contact angle is zero, cos is 11 dyne imparts an acceleration of 1 cm/secto a mass of 1 gramor an acceleration of g = 981 cm/secto 0.00102 grams force 2 2 72.8g d gf00102.0 223 2 2 ssgs 728 rcos2hc inrfor(cmr0.15scm980g1s 72 . 8 g2rcos2h222cr 17 Grain size distribution: e r than ing % finer than c reasing % coars e Decreasing grain size increas Estimate the height of capillary rise for water in sand.Grain size distributions in Fetter (pg74-75)Smallest ~ 0.08 mm 10% ~ 0.17mm = 0.017cmWhat if the soil is a silty sand?Grain size distributions in Fetter (pg74-75)Smallest ~ 0.002 mm 10% ~ 0.017mm = 0.0017cm 2 d iltd h 2 hc What if the fluid is gasoline?Substance Surface Tension (dyne/cm)Water 72.8 dyne/cm Gasoline ~33 dyne/cm (note tension for water)specific weight? check the web (~0.68 density of water)ich will dominate, surface tension decrease or specific weight decrease? san y san d 18 Thus far we have looked at fluids with a contact angle near zeroand the cosine of zero is one, so we have not had to consider it cos 2 Some fluids have a contact angle approaching 90and that needs to be considered in estimating capillary rise r cos 2 h c For a nonwetting fluid that angle will result in a depression rather than ris e What is theMAXIMUM HEIGHT (in feet) THAT YOU CAN RAISE WATER BY SUCTION? NOTE: IT IS LIMITED BY THE PREVAILING ATMOSPHERIC PRESSURE so choose your locationsea-level ~14.7, Denver ~12.2, Mexico City ~11.1, Mt. Everest ~4.9) h:Recall P